Problem: What is the area, in square units, of triangle $ABC$? [asy]
unitsize(1.5mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;

pair A=(-3,1), B=(7,1), C=(5,-3);
pair[] dots={A,B,C};
real[] xticks={-4,-3,-2,-1,1,2,3,4,5,6,7,8};
real[] yticks={3,2,1,-1,-2,-3,-4,-5,-6,-7};

draw(A--B--C--cycle);
dot(dots);

label("A(-3,1)",A,N);
label("B(7,1)",B,N);
label("C(5,-3)",C,S);

xaxis(-5,9,Ticks(" ", xticks, 3),Arrows(4));
yaxis(-8,4,Ticks(" ", yticks, 3),Arrows(4));
[/asy]
Explanation: Use the area formula $\frac{1}{2}(\text{base})(\text{height})$ with $AB$ as the base to find the area of triangle $ABC$.  We find $AB=7-(-3)=10$ by subtracting the $x$-coordinates of $A$ and $B$.  Let $D$ be the foot of the perpendicular line drawn from $C$ to line $AB$.  We find a height of $CD=1-(-3)=4$ by subtracting the $y$-coordinates of $C$ and $D$.  The area of the triangle is $\frac{1}{2}(10)(4)=\boxed{20\text{ square units}}$.

[asy]
unitsize(2mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;
pair A=(-3,1), B=(7,1), C=(5,-3), D=(5,1);
pair[] dots={A,B,C,D};
real[] xticks={-4,-3,-2,-1,1,2,3,4,5,6,7,8};
real[] yticks={3,2,1,-1,-2,-3,-4,-5,-6,-7};
draw(A--B--C--cycle);
dot(dots);
label("A(-3,1)",A,N);
label("B(7,1)",B,NE);
label("C(5,-3)",C,S);
label("D(5,1)",D,N);
xaxis(-5,9,Ticks(" ", xticks, 3),Arrows(4));
yaxis(-8,4,Ticks(" ", yticks, 3),Arrows(4));[/asy]